Download Assignment 9.

ELECTRIC AND MAGNETIC FIELDS
ASSIGNMENT 9
Questions 1 - 3 count for 95% of the marks and Question 4 for 5%.
Q1 A 10-turn square coil of wire has sides of length 5 cm and
carries a current of 2 A.
Y
(a) What is the magnitude of the magnetic moment vector
of the coil?


The plane of the coil is inclined to the x-axis, with an angle 
between the magnetic moment vector and the x-axis, as shown.
A magnetic field of magnitude 2 T points along the +x axis.
X
coil seen edge-on
(b) Find the magnitude and direction of the torque on the dipole.
(c) The dipole can rotate about an axis parallel to the z-axis, and it comes to rest in it
equilibrium position. Draw a sketch showing the orientation of the dipole moment
vector in the equilibrium position.
(d) Starting from the equilibrium position, an external torque is applied in order rotate the
dipole. Find the work needed to rotate it through 1800.
Hint: The work done when a torque  is applied over an angle d is d.
Q2 A long copper pipe has inner radius a and outer radius b. It carries
a current which is uniformly distributed over its cross sectional area
between a and b, with current density (i.e., current per unit area)
equal to J. Use Ampere’s Law to show that the magnitude of the
magnetic field as a function of radial distance r from the axis is
given by
 J( r 2  a 2 )
for a < r < b
B  0
2r
and
 0 J (b 2  a 2 )
B
2r
a
b
for r > b.
Sketch the variation of B with radial distance, starting from r = 0.
Q3 Two conducting coils are placed close together such that their mutual inductance is 5 mH.
One of the coils is connected to a current source whose time-varying current is given by
I1(t) = 2(1 - e-10t)sin(100t)
A
where t is the time in seconds.
(an oscillating current whose amplitude increases and settles down to a value of 2 A).
(a) What is the magnetic flux through the second coil at t = 0.10 s ?
(b) What is the magnetic flux through the second coil at t = 0.11 s ?
(c) What is the emf induced in the second coil at t = 0.10 s ?
(d) What is the emf induced in the second coil at t = 0.11 s ?
(e) Write down the equation for the induced emf for very large values of t.
Q4 A very large thin conducting plate lies in the x-y plane. Current flows in the y direction such that
the current crossing the x-axis is  A m-1.
Z
Very large conducting plate
Y
Current flows in x-y
plane in the y-direction
X
Use Ampere's Law to show that the magnitude of the magnetic field at a point above the plate
is given by
B = o/2.
Hints:

Draw a diagram of the system as seen from a point of view such that the current
flows straight out of the page.

The magnetic field lines are parallel to the x-y plane (think about why this must
be so).

Define a suitably shaped path for applying Ampere's Law.